In this talk, I describe the problem of determining whether a given language is weakly definable. In particular, I present recent work showing that given a Büchi automaton as input, it is decidable whether the language is weakly definable. The proof is by reduction to a boundedness problem for cost automata (a form of automata with counters).

Joint work with Thomas Colcombet, Denis Kuperberg, and Christof Löding.